How do I do this question? I just started self-learning number theory as recreation so yeah if anyone can show me how to solve it, I would really appreciate it.

I understand that you are doing mathematics recreationaly and that you just want to see the solution so that you better understand the topic, but that being said I would like to quote the mathematician George Simmons: "Despite our vast advances in mathematics, nothing has replaced the necessity of problem solving."

So, what have you tried?

January 2nd 2010, 09:30 AM

NonCommAlg

note that the sequence is strictly increasing and also we may assume that suppose that the claim is false. so there exists some such that is prime for all

choose large enough so that see that and for all integers let where now, if

choose and if choose see that which is a contradiction.

Note: i left a couple of thing for the OP to discover, so Drexel28 wouldn't get too mad at me!